Proton Radius from Muonic Hydrogen Spectroscopy and Effect of Atomic Nucleus Motion

The proton radius has been measured in electron-proton scattering experiments and laser based spectroscopy of muonic hydrogen. The latter method is based on the precise calculations for the atomic energy levels in the approximation of static nucleus, and includes numerous corrective effects.The 4% discrepancy between two measuring methods is known as the proton radius puzzle. We suggest that this discrepancy may be caused by an additional electromagnetic interaction with the magnetic moment generated by then ucleus motion around the center of mass of the muonic hydrogen. The scale of this effect is estimated based on the known hyper fine structure of the muonic hydrogen. Our estimation show that the effect of the atomic nucleus motion is high enough and may help to solve the proton radius puzzle